gnuplot - 2d interpolation, don't explicitly list x-values

I would like to generate using GNUPlot, a 2d plot from a list of y-axis values, without stating explicitly the corresponding x-value. In other words, I do not have

but instead have

5 10 3 5 6 14 (y-values listed only, not x values)

How can I generate a 2d plot from this, by specifying only the bounds of x, assuming uniforming spacing, and not explicitly listing x?

Then I would like to interpolate the y-values

Solution

You could use the 0 pseudocolumn for this:

   column(0)   The sequential order of each point within a data set.
               The counter starts at 0 and is reset by two sequential blank
               records.  The shorthand form $0 is available.

In order to start counting from 1, the example below uses ($0+1). If needed, a more general form would be $0*step + xMin, where xMin denotes the required minimum value of x and step stands for the step size (spacing of individual x values).

unset key

$data <<EOD
5
10
3
5
6
14
EOD

fit (a*x + b) $data u ($0+1):1 via a,b

plot \
    $data u ($0+1):1 w lp, \
    a*x + b w l lc rgb 'red' lw 2